On the optimality of dolinar’s receiver

Dolinar’s receiver is an architecture for distinguishing between two possible coherent states, using a photon detector and a local signal which may depend on past detector measurements. The optimal local signal satisfies very favorable properties: it is independent of the time horizon, and the resulting error probability is independent of the measurements. It was also shown that the same signal is optimal in the sense of maximizing the mutual information between the identity of the state and the measurements. In this work we show that the same signal is optimal for the optimization of the expected value of a wide class of objective functions. Our proof is based entirely on convex optimization and functional analysis, without resorting to any “quantum” arguments.